Maximum Norm a Posteriori Error Estimation for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations

Abstract

In this paper, a system of singularly perturbed semilinear reaction-diffusion equations is discretized on an arbitrary nonuniform mesh using an upwind finite difference scheme. Based on the quadratic polynomial interpolation function, a second-order maximum norm a posteriori error estimation is derived. Then, this bound is used to design an adaptive grid generation algorithm. Numerical results are given to verify the effectiveness of the presented adaptive grid method.<br />